This work solved a new two-objective scheduling problem of n jobs considering past-sequence-dependent setup time (PSD) and learning effect (LE) on a single machine. Although researchers gradually consider PSD and LE, there is none who deals with both effects in the bi-criteria problems. The reason is that multi-objective problem is harder than a single objective problem because we need to acquire Pareto solutions. As a result, this paper is the first one who solves this issue. We considered two objective functions. To tackle with this new problem, we proposed a method to solve it effectively. We first analyzed the parameters according to the weights on each position of the two objectives. Then, we matched the weights with the processing time of the jobs. So that two optimal sequences were obtained by this matching approach. In addition, we started to search a new Pareto solution located between the two new solutions. The process was repeated to search a pair of solutions until no new solutions were found. Our approach was very efficient to find out the minimum set of optimal sequences (MSOS). To evaluate the proposed method, we compared it with the benchmark multi-objective algorithm, MOEA/D, on numerous instances. The empirical results had shown the proposed algorithm was effective when searching a set of approximate solutions in a very short CPU time when it was compared with MOEA/D. This proposed algorithm was promising to deal with the two-objective scheduling problem in this research.
